Vectors - The Dot Product

[JustinChuaCHee]

indeed solved my doubts. thank you for your video!

[liverallstrong]

sucks to be left handed, unless you live in some country where they write from right to left. Or if you are hardcore you can learn to write backwards like Da Vince.

[patrickJMT]

@liverallstrong it has really held me back all my life. really. it is tough.

[cliffordude0627]

very useful thank you



[Rishi1234321]

you should make your own religion

[patrickJMT]

@Rishi1234321 yuck, no thanks

[ThePurplebarney]

I was ready to hit my head against a wall when I couldn't get what my professor was talking about. Your videos have literally saved my life! Thank you soo much! :]

[pokos33]

What would you do if you've got the component of axb (x is times, not the letter in this case), and the dot product of a and b, and you need to get the angle? I've asked around my campus, but no one seems to be able to explain it properly or in a way that I can understand.

[jax777987]

Oh at the end of the video when he mentioned orthogonal, just magic. Verbatim what I needed to know. Gorgeous

[DarkCeremony]

thanks, i get it now.

[gingerbredm4n]

i was doing my calculus final work and i forgot how to do this stuff and you.saved.me.soooo.much time i cant thank you enough:)

[Bakugantsuvai1]

Hey what is the tittle of the magnitude video?

[JurisL85]

Thanks a lot, you def. have what it takes to teach! I am programming my Vector2D class in C++ for my 2D game engine right now as i watch this video! Thanks again!

[alexmusicgraffity]

"Patrick shud do Fizzics Videoz" Says my cat

[Dtjuh91]

Hi, I'm from Holland,

do you know if this math is the same in europe as it is in America?

[patrickJMT]

@Dtjuh91 i do not think i understand your question

[Bakugantsuvai1]

@patrickJMT He is just asking if this method applies all around the world (I think it does)

[DjChopstyk]

@Dtjuh91 Math is a universal language, there may be many different methods but I'm pretty sure the math in China is the same as the math in the United States. Meaning it would be the same in Holland.

[Bakugantsuvai1]

@DjChopstyk But in China math is harder, making it tougher for kids in China (Asia). So thank god that we get to use calculators since Chinese are banned from calculators.

[musefoshizzle]

@Bakugantsuvai1 at my college, calculators are banned in all math classes except statistics

[keenkennyny]

@Dtjuh91 just like music math is universal. Everyone uses calculus, trigonometry, geometry, etc but math might be taught different using different methods even on the national level. A teacher on one side of America may teach how to solve a problem differently from a another teacher right next door, but the answers should be the same.

[gingerbredm4n]

@Dtjuh91 math is the same anywhere in the world. numbers dont change...

[meecheekitten]

@Dtjuh91 math is a universal language. it's the same conce

[meecheekitten]

@meecheekitten concept*

[hvhfyjtdhf]

@Dtjuh91 I believe it is generally the same everywhere, I'm from Asia and I find these vids really useful

[KillerZero259]

why do you use the inverse of cos and not the inverse of the other trig functions?

[wackawacka060606]

im in calc 3 and i came back to review this lol. thx

[soulxofxgirl]

very useful video

[tiffanyarmani1]

Does it matter if the vector is up and down instead of across?

ie. Taking the dot product and cross product of the following vectors

u = [1 2  3],

v = [4 5 6]

[TheFatmash]

thank youuuu 

[theDgrader]

thanks PJ, i went through the theory and got bogged down, you have helped allot in understanding a few gray area's.... thank you sir

[patrickJMT]

@theDgrader no problem, happy to help

[Elzelgator]

dot product is it it vectoral??

[SynpaticInc]

You are a life-saver! I can't believe you have physics videos also. Thank you so much for taking the time to explain these concepts!!

[patrickJMT]

@SynpaticInc happy to help! : ) not a ton of physics stuff, just stuff mainly related to vectors

[fidelsalgado]

Nice job! Really useful

[JamesK89]

Awesome! You're a member of the master left handed race. Lefty high five!

[rawna1]

great video, thanks alot this helped alot :)

[patrickJMT]

@rustyshackleford54 there is a video on that somewhere.... if they are parallel they are simply multiples of each other!

[cogle9469]

And Patrick said "Let there be light" and so it was. Proof that Patrick is a god

[Gaiacarra]

Why does every teacher just introduce the dot product like it's the most natural thing in the world? It's such an obscure concept, why invent an operation for it? I know it comes up a lot, but so does the Pythagorean theorem, but we haven't got a "pythagorean product" that's equal to the square of the sum of the squares of its operands. It just seems so pointless and obtuse.

[Gaiacarra]

@Gaiacarra *root of the sum of the squares

[blightedpersona]

why the hell was this same exact lesson so difficult to understand 2 hrs ago when i was in class? damn I wish i had useful professors...

[tkatiqah]

NOT TO COMPARE BUT BETTER THAN KHAN ACADEMY!!!!

[tkatiqah]

YOU ARE THE BEST!!!!!!

[greendayosmness]

hey thnks fr a wonderful vid! it ws rly helpful...

jus a lil question ive got here...

is this multiplication (dot / cross product) limited til 3 dimensions only? or can we apply it further?

:)

[NiCoLeY7567]

im taking the physics sat ii in october and i really want to get a perfect score. your explanations really simplify the subjects i have to review =] thank you

[nikvenkata]

P-JAMMMMMM!!!!!!

[deesharkz]

taking a physics class over the summer and were required to know learn vectors on our own. These videos have been very helpful, thank you.

[krashiyer]

r u born intelligent or r u born god?

[sammyy07]

i think this just saved mee!!!! thank you so much!

[letthemxeatcake]

Man you are a life saver!

[AshleyReneeHA]

I love you!

[theyasin33]

What is the difference between a dot product and cross product? I know dot is a scalar and cross is a vector but why are they that?

[peachcoloredpimple]

Patrick JMT please marry me!! I would be the luckiest girl alive!

[seiparc]

i really love your tutorials.

[ramirezbrandon25]

how do u know if its parallel?



[kirbypwnsyou]

@ramirezbrandon25 if the vectors are equal then that means they are either the same line or parallel

[brawl313]

@ramirezbrandon25 I think that if their cross product equals 0 they're parallel

[jamiekim093]

ur the number one tool when it comes to cramming for my tests! thank you!

[Crowe0920]

I caan't believe i'm saying this: but Youtube is teaching me calculus better than my college professor :O

[BusyNames]

Thank you! Very well explained

[ravishlystunning]

Wow man awesome..dats awsm thanku thanku!!!!!!!!! :)

[Username93611]

I've never seen anyone put that hook on the end of the radical symbol before. Who did you learn that from?

[patrickJMT]

@Username93611 just something i started doing on my own to help my brain clarify what is under the radical, and what is not.

[ben73h]

@patrickJMT Hi Pat, Why I click n this video, there is a advertisement ? How can I get rid of thid advertisement ? please show me. Thanks.

[NiCoLeY7567]

@ben73h popular youtubers usually let youtube advertise on their videos to earn money. this is because people who watch videos on this website don't have to pay. there is no way to skip over the advertisements (unfortunately) but some let you skip a part of it after a few seconds...you can't choose which ones though

[sergefabregas]

thankyou so much this video helped

[EMOtions12]

i honestly cannot thank you enough...

[TelsaBom]

Hi Patrick. Do you have any videos on the distinction between these three vector problems? Cheers.

a  (b x c)

a  (b + c)

a x (b + c)

[Rxoxoxo56]

Since i didnt go to classes the whole term, you video was the only way to get an A in the course, and it worked! Thanks a lot :)

[Shocker9]

At 0:50 you state a theorem. cos(theta) = (a.b)/ (|a|.|b|)

What is this theorem called? I've tried looking for the name of this theorem but i can't seem to find it. Great video by the way.

[Shocker9]

I've just realised that the theorem doesn't have a name, as its just a relationship to do with the dot product.

[moondragon05]

holy shit man, your videos are awesome i was so confused before, but now that i've watched your videos i might pass my vectors test tomorrow after all and make it to university :D

[patrickJMT]

@moondragon05 good luck!

[IiAashirIiK]

Thankss alot vid was very helpful

[Lexzile1]

-__- It was just a joke. Sorry thought you would find it funny. =P

Love your videos! Keep up the good work. ;)

[Mikej1592]

by far, this was the most helpful video explaining this that I have found in two days of searching, thank you so much. It makes me wonder why the eff didnt they just write it like this in the dang calculus book for school? the book trys to go into the theory or some crap, I learn by give me the formula, tell me what to put where and then tell me what it is that I am doing. I read the teachers notes, (online class) the book sections 3 times and this video was infinitly more helpful. thanks!!!

[TheIBGEEK]

What is a column vector and is (x,y) the same thing as if it were shown like a matrix oh and is there such thing as a row vector, how would it look like (sorry if i added the question mark it wont post)

[syedfarukh3]

heyy...a question?

why is dot product a scalar quantity??

this might be a simple question but i cant get my head round it....

[NiCoLeY7567]

@syedfarukh3 i think it's just the way it is. you can get the vector quantity but it would no longer be called the dot product but rather the cross product. just names like "speed" and "velocity". one tells direction and the other doesn't. I'm not sure though

[chromagnonbc]

When is it advisable to use radians rather than degrees? thanks in advance since I'm having trouble figuring that out. (P.S. your videos saved my ass over and over again, thank you so much and keep it up :D )

[patrickJMT]

@chromagnonbc well, people tend to always use radians in calculus - that is just the convention.

[chromagnonbc]

@patrickJMT thank you very much!

[frendlyghst007]

I'm struggling in math right now...trade brains with me!!!

[Soulscarz]

i heart you, will you be my valentine?

[patrickJMT]

@Soulscarz thanks for the offer, but i am spoken for.

[FaiththeHairstylist]

OMG. I was doing this correctly, but my arithmetic was off, so I thought I was doing it wrong!!! I'm so glad when I make stupid mistakes . . .at least I know I understand the higher concept even if I don't know how to add correctly. :)

[Mikej1592]

@FaiththeHairstylist Your comment was hilarious, and I so feel your pain, and isnt it ironic to understand the complex calculus and make mistakes in the basic math? :-) In a way its like being an excellent driver but have no idea how to put gas in the tank. hehe. I on the otherhand had no idea what the book was talking about but his video really makes it easy to understand. not like my condesending teacher that cant explain it because she cant stop telling us how dang easy this stuff is.

[kx32ta1]

Does having an add before your video mean you've hit the big time? You are a life saver by the way!

[damienjeffgomez]

Thank you...

[BrAyDeN2593]

Thanks so much! This helped a lot.

[sirshaunathan]

thank you sooo much!

[SDTricker]

I don't care about the Oprah show!!!! I want to watch the dot product!!!!!!

[LacysMomSong]

Thank you so much!!! Trying to help my daughter get through trig and it's been 30 years since I've done it! Great explanation and great help getting me back up to speed in trig and physics!

[ZFero]

You and Salaam Khan should be in charge of the Canadian and American Education system. 

[patrickJMT]

@ZFero i would not have the first clue as to what to do

[gloopybuger108]

@patrickJMT first thing you should do is order pizza using the money reserved for public education.

[afgibnasina]

@patrickJMT

I watch your videos and you explain the steps well but for slow math mind like mine; it sounds fast. I have not studied math for 10 years and I use your math videos to study for CSET Math for CA. I want to be a middle school teacher. The reason people do not learn math in American is social dogmas one and second teachers do not set the anticpatory setting. (math is important because..)

[multipurpose101]

0:38 i KNEW it was "if and only if" rather than simply "if" ...should've corrected my Physics teacher right away...anyway, thanks Mr. Patrick!

[Enceladus187]

There are 3 kinds of math profs. Those that want you to think they are really smart so use terms and go at a pace purposefully over your head. The second type thinks they are too important to teach and give no effort whatsoever. And the third which dont care about looking smart, they only want to share the beauty of math with those that have the will to study it. Euler was a teacher of this manner and PatrickJMT is no different. He is the man.

[drewpasttenseofdraw]

Praise be to the man that allows his dynamics to be paused and written down and dwelt upon. If I could pause and rewind and search my professors mind, then I would be praising his glory too. Thank you for pause-abale systematic explanations they help shed light.

[scarykidbryan]

Your videos of very helpful. You inspired me to make my "easily memorize the unit circle" video. You should make videos on DISCRETE MATH! There are barley any videos of discrete math on youtube. Then again idk if you're into comp. sci.

[patrickJMT]

@scarykidbryan i bought another book this weekend on discrete math (my favorite stuff!) so i probably will eventually. there are still like a million videos i want to make, but my busy day job prevents that

[aabhas11111]

Man I Love Studying Maths ........ All These Academic Pressures Make Me Sick.....

I Love Studying Maths Here Cause It's Interesting And Thats How It Should Be Everywhere Else !!

[aloich39]

so many science ppl are left handed...

[Bronnil858]

Patrick, I dont understand the dot product, I mean I know how to find it and everything but I dont understand what it is.

You say its a scalar but a scalar of what, whats the point of it.

[coopergurl90]

patrick, i owe the degree i am pursuing to you! You make math for me! -For that I thank you...

[jwmcmac]

so far . . . no one that teaches dot product seems to 'know' or 'care' what it actually represents . . . proving it or not being beside the point . . . it is a scalar . . . it has to do with the projection, I think, of one of the vectors onto the other. It divided by the magnitudes of the same vectors, represents the ratio of cosine of theta . . . in disguise of some sort . . . so it is the numerator of the cosine ratio of the angle in question . . . but what is it, really? You may know.

[jerryboland2008]

thank you for such clear presentations!

[komal517]

please teach at rutgers university.

[patrickJMT]

@komal517 they would not want me, i have no phd, so could not pull in the big research dollars. universities do not actually care if you can teach or not.

[ownedncut]

@patrickJMT haha go for the PHD dude!

[patrickJMT]

@ownedncut i worked on it for one year and left. that life is not for me.

[Lexzile1]

@patrickJMT

if it strenous? is it worth it?

[mrmts]

@patrickJMT too true.

[futbolplayercr7]

@patrickJMT Why do they not care if an instructor can teach or not?

[sirshaunathan]

Thank You SOOO much!

i was slacking with my notes, and didn't have this the dot products and vectors

!thanks

[patrickJMT]

@ProMysteryGuy maybe your mask scares him so that he is in a hurry to get out of class

[svalmazan]

please be kind enough to let me know how the expression for the multiplication of the dot product of two vectors a and b was arrived at. i am sorry but i am not familiar with mathematical theorems, i am trying to help out my daughter in high school in her math subject. thank you so much.

[patrickJMT]

@svalmazan if you mean the a dot b = a b cos theta part, it is proved in any calculus text book; basically one uses the law of cosines to arrive at the result

[AlexDuude]

Awesome video I subscribed.I learned more from you from 1 video than I did an entire year with my math teacher

[t00smartc00kie]

i am eternally grateful for your physics genius and for helping me out so much

[patrickJMT]

@davoho yes, it seems under lots of circumstances and one day in the future, lots have promised me many things. i will not be holding my breath though!

[orangeman9]

the 2 people who disliked this must be emo! and just failed calc!

[patrickJMT]

@orangeman9 ehehehh, its the internet! i am surprised anyone likes it at all!

[Q8RedDevil91]

you could've took radical 49 to be 7 , rather than multiplying it with radical 3 to get a crazy number !!?

[musa78692]

Thankyou patrick

[musa78692]

Thankyou patrick

[livinglinkz]

you.....are the man.

[patrickJMT]

@livinglinkz just doin' what i can

[Paumonsu]

Which is the meaning of a dot product being negative or positive?

[Isurrendertoyou]

Thanks so much! I finally understand the Dot Product!

[XxNaSaHxX]

Lefty, fuck yes!

[lospepes14]

Orthogonal?? Who the hell uses that??

[SnowmenArePimps]

subscribed, Favorited, and T-Up

i finally understand these Dot Product calculations :P

thanks

[Ilikemustard]

You teach so much more clearly than my lecturer... So much easier to understand now

[patrickJMT]

@Ilikemustard great!

[rosicky1992]

dude ur writing with ur left hand

[Valecrier]

So easy to understand. You're way better than my teacher. Thanks so much for uploading this.

[Xlenia]

why do we square the numbers in the denominators (the magnitude) @ 4:24?

[bnel890]

my teacher teaches differently from the book i use, and neither the book, nor the teacher teach well. I thank you greatly for your videos.

[hostilekid21]

Two words... LIFE SAVER.

[B1U2S3H4R]

thank you, I'm in college and this video was a nice reminder of what we took in high school

[2ris2]

Thanks, my math teacher is going to teach this to us tomorrow, :) I will probably get a head start on this! Thanks for the video.

[suivzmoi]

i dont know why you even upload all these videos but God bless you.

[VangY34311]

be my professor

[madscirat]

Great video, thanks.Using dotproduct to find the angle between two vectors was not something I had thought of doing.

[xxKrazy2nRxx]

man seriously, anytime I have confusions on calc your video clear it up....keep it up...=)

[zasabiibasaz]

who would download this ROFL

[mjifishman]

people who are trying to educate themselves. so basically the opposite of you

[patrickJMT]

get used to hearing this: i will take fries with that...

[ownedncut]

@patrickJMT

haha patrick.. my calculus teacher in grade 11 would staple MCDONALD JOB APPLICATIONS to the back of kids' tests. (The ones who did poorly /didn't care)

[orangeman9]

@zasabiibasaz  who would download this? a smart person who wants to learn math...... DUH! *cough* idiot *cough*

[avthemagnificent]

ur the best !

[priyakoko]

amazing explanation

[rjr343]

If there is a greatest of all time for math teaching you come in second to none!!!! thankyou thankyou thankyou

[tony225]

Writing on a dry-erase board as a lefty must be a pain.

[bubulala5]

GREAT JOB!

[aniii123]

Wow, thank you SO much for posting these videos! You're outstanding at explaining!!!! :]

[Dancesux]

but what is the dot product

[redzor812]

its a scalar

[MetallicaFTW7]

@redzor812 yeah, what is a scalar? haha

[suckbar69]

@Dancesux Unfortunately no one can be told what the dot product is.. you have to see it for yourself. Oh wait, he just did.